On the Gauss map of minimal Lorentzian surfaces in 4-dimensional semi-Riemannian space forms with index 2


Canfes E. , Turgay N. C.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.91, pp.349-367, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 91
  • Publication Date: 2017
  • Doi Number: 10.5486/pmd.2017.7643
  • Title of Journal : PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Page Numbers: pp.349-367

Abstract

In this paper, we study minimal Lorentzian surfaces with finite type Gauss map in 4-dimensional semi-Riemannian space forms with index of 2. First, we give the complete classification of Lorentzian surfaces in the semi-Euclidean space E-2(4) with pointwise 1-type Gauss map. Then, we study all Lorentzian minimal surfaces in S-2(4) (1) regarding their Gauss map. In particular, we proved that a Lorentzian minimal surface in S-2(4)) has 2-type Gauss map if and only if it has constant Gaussian curvature and non-zero constant normal curvature.